# Volumetrically Consistent Implicit Atlas Learning via Neural Diffeomorphic Flow for Placenta MRI

arXiv: https://arxiv.org/abs/2603.16078 · HTML: https://mlsanity.com/paper/2603.16078/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 45 references that are in the map.
- First posted on arXiv 17 Mar 2026.

## Builds on (most cited first, 24 of 24)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [PIFu: Pixel-Aligned Implicit Function for High-Resolution Clothed Human Digitization](https://mlsanity.com/paper/1905.05172/) (2019)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)
- [Unsupervised Learning of Probabilistic Diffeomorphic Registration for Images and Surfaces](https://mlsanity.com/paper/1903.03545/) (2019)
- [Deformed Implicit Field: Modeling 3D Shapes with Learned Dense Correspondence](https://mlsanity.com/paper/2011.13650/) (2020)
- [Fast Symmetric Diffeomorphic Image Registration with Convolutional Neural Networks](https://mlsanity.com/paper/2003.09514/) (2020)
- [Deep Implicit Templates for 3D Shape Representation](https://mlsanity.com/paper/2011.14565/) (2020)
- [SimCVD: Simple Contrastive Voxel-Wise Representation Distillation for Semi-Supervised Medical Image Segmentation](https://mlsanity.com/paper/2108.06227/) (2021)
- [Recurrent Mask Refinement for Few-Shot Medical Image Segmentation](https://mlsanity.com/paper/2108.00622/) (2021)
- [Curriculum DeepSDF](https://mlsanity.com/paper/2003.08593/) (2020)
- [Neural Mesh Flow: 3D Manifold Mesh Generation via Diffeomorphic Flows](https://mlsanity.com/paper/2007.10973/) (2020)
- [AFTer-UNet: Axial Fusion Transformer UNet for Medical Image Segmentation](https://mlsanity.com/paper/2110.10403/) (2021)
- [Topology-Preserving Shape Reconstruction and Registration via Neural Diffeomorphic Flow](https://mlsanity.com/paper/2203.08652/) (2022)
- [Unsupervised Wasserstein Distance Guided Domain Adaptation for 3D Multi-Domain Liver Segmentation](https://mlsanity.com/paper/2009.02831/) (2020)
- [Diffeomorphic Image Registration with Neural Velocity Field](https://mlsanity.com/paper/2202.12498/) (2022)
- [MultiMorph: On-demand Atlas Construction](https://mlsanity.com/paper/2504.00247/) (2025)
- [Placental Flattening via Volumetric Parameterization](https://mlsanity.com/paper/1903.05044/) (2019)
- [Hybrid Neural Diffeomorphic Flow for Shape Representation and Generation via Triplane](https://mlsanity.com/paper/2307.01957/) (2023)
- [Volumetric Parameterization of the Placenta to a Flattened Template](https://mlsanity.com/paper/2111.07900/) (2021)

## Abstract (arXiv)

Establishing dense volumetric correspondences across anatomical shapes is essential for group-level analysis but remains challenging for implicit neural representations. Most existing implicit registration methods rely on supervision near the zero-level set and thus capture only surface correspondences, leaving interior deformations under-constrained. We introduce a volumetrically consistent implicit model that couples reconstruction of signed distance functions (SDFs) with neural diffeomorphic flow to learn a shared canonical template of the placenta. Volumetric regularization, including Jacobian-determinant and biharmonic penalties, suppresses local folding and promotes globally coherent deformations. In the motivating application to placenta MRI, our formulation jointly reconstructs individual placentas, aligns them to a population-derived implicit template, and enables voxel-wise intensity mapping in a unified canonical space. Experiments on in-vivo placenta MRI scans demonstrate improved geometric fidelity and volumetric alignment over surface-based implicit baseline methods, yielding anatomically interpretable and topologically consistent flattening suitable for group analysis.